Trains that are just called "express" are different from a Limited Express, and most likely have only unreserved seating. These are commuter trains that skip over some of the smaller stations, rather than trains that travel long distances. Some examples include the "JR Rapid Express" that carries students and workers between Osaka and Kyoto cities in Kansai, or Tokyo and Yokohama cities in Kanto. You do not need to make reservations for express trains, although you may find that these are very crowded
during peak rush hours.